Uniform one-factorisations of the complete bipartite graph
Last modified: Sept. 5, 1996
Joint work with Gillian Nonay with significant contributions from Dan
Archdeacon and Gordon Royle. Thanks to Cindy Lau for help in setting up
these Web pages.
These pages are still under construction. In particular, the table is
incomplete; some known examples remain to be entered.
Select items from the table at left.
The table at left lists, for 2<=n<=11, all possible partitions
of the integer n into parts of size larger than one. For example,
the partition of 8 into 3+3+2 is encoded
as [3,3,2]. For each such partition [k1,k2,
...,ks], we ask "Is there a one-factorisation of
the complete bipartite graph Kn,n
having the property that the union of any two distinct one-factors is
isomorphic to a 2-regular graph having components of size
2k1, 2k2,..., 2k1?" The
table indicates "Yes" if an example is known, "No"
if it is known that no example exists, and "?" in the remaining
cases. If one clicks on any link in the table, an example, construction,
or non-existence argument appears in the frame above.